Non-linear filtering for the reconstruction of a surface electrocardiogram from an endocardial electrogram

ABSTRACT

An active medical device using non-linear filtering for the reconstruction of a surface electrocardiogram (ECG) from an endocardial electrogram (EGM) is disclosed. The device for the reconstruction of the surface ECG includes a plurality of inputs, receiving a corresponding plurality of EGM signals from endocardial or epicardial electrogram (x 1 [n], x 2 [n]), each collected on a respective EGM derivation of a plurality of EGM derivations, and at least one output delivering a reconstructed surface ECG electrocardiogram signal (y[n]), related to an ECG derivation, and a non-linear digital filter ( 12′, 12′, 14 ) with a transfer function that determines the reconstructed ECG signal based on said plurality of input EGM signals. The non-linear digital filter includes a Volterra filter type ( 12, 12′, 12 ″) whose transfer function includes a linear term (h 1 ) and at least one quadratic (h 2 ) and/or cubic (h 3 ) term(s).

CROSS-REFERENCE TO RELATED APPLICATIONS

This present application is a continuation of U.S. application Ser. No.14/021,890, filed Sep. 9, 2013, which is a continuation of U.S.application Ser. No. 12/731,009, filed Mar. 24, 2010, which claims thebenefit of French Patent Application No. 0901399, filed Mar. 25, 2009.U.S. application Ser. No. 14/021,890, U.S. application Ser. No.12/731,009, and French Patent Application No. 0901399 are incorporatedby reference herein in their entireties.

FIELD OF THE INVENTION

The present invention relates to “implantable medical devices” such asthose defined by the Jun. 20, 1990 Directive 90/385/EEC of the Councilof European Communities, specifically to implantable devices thatcontinuously monitor heart rhythm and deliver to the heart, ifnecessary, electrical stimulation pulses for cardiac resynchronizationand/or defibrillation.

The invention more particularly relates to processing the signalsrepresentative of cardiac depolarization potentials of the myocardium,such signals being collected through epicardial or endocardialelectrodes for pacing, sensing or defibrillation of the right and leftatria or ventricles, of these implantable devices.

Even more particularly, the present invention is directed to a method,whether or not implemented in that implanted device, for thereconstruction of a surface electrocardiogram (ECG) from an endocardialor epicardial electrogram (EGM).

BACKGROUND OF THE INVENTION

It is known that EGM signals are collected by use of electrodes placedon endocardial or epicardial leads of a device implanted in a patient.These signals, directly related to electrical activities of cardiaccells of the patient, provide much useful information for the purpose ofassessing the patient's condition. Hence, after amplifying,conditioning, digitizing and filtering, EGM signals are mainly utilizedto control the implanted device and diagnose rhythm disorders requiring,for example, automatic triggering of an antitachycardia,antibradycardia, or interventricular resynchronization therapy.

However, when it comes to analyzing subjectively the cardiac rhythm,e.g., to perform a diagnosis or to readjust the control/operatingparameters of an implanted device, practitioners prefer, in practice, tointerpret the information given by a surface electrocardiogram (ECG). Asurface ECG allows one to visualize in a direct manner, certaindetermining factors (e.g., QRS width) and thereby assess the evolutionof a cardiac failure.

ECG signals are usually recorded over a long period of time throughambulatory practice by Holter recorders. The recorded ECG signals arethen further processed and analyzed in order to evaluate the clinicalcondition of the patient and eventually diagnose whether a cardiacrhythm disorder is present.

The ECG and EGM signals actually have the same signal source, i.e.,electrical activities of the myocardium, however they visually appear inmuch different manners: the EGM collected by the implantable deviceprovides local information on electrical activities of a group of heartcells, whereas the ECG appears in the form of more global information,in particular influenced by the propagation of electrical signalsbetween the myocardium and body surface with certain morphologic andpathologic specificities. Thus, the display of EGM signals is not veryuseful to a practitioner who interprets ECG signals.

When a patient implanted with a medical device comes to his/herpractitioner for a routine visit, two distinct devices are used: an ECGrecorder and an external implant programmer. In order to collect ECGsignals, the practitioner places electrodes in particular locations ofthe patient's torso. The ECG signals are collected between predefinedpairs of electrodes to define typically twelve derivations of thecollected ECG signals. The external programmer is used to controlcertain operating parameters of the implanted device (e.g., the batterylife), download data from the memory of the implantable device, modifythe parameters thereof, or upload an updated version of the deviceoperating software, etc.

The visit with the practitioner therefore usually requires two differentdevices, as well as specific manipulations for placing the surfaceelectrodes and collecting the ECG signals.

Moreover, the use of these two devices requires the patient to come to aspecifically equipped center, usually having the consequence thatroutine visits are spaced farther apart, resulting in a less rigorousfollow-up of the patient.

Furthermore, the ECG recording has various drawbacks, notably:

-   -   the preparation of the patient which requires a certain time,        correlated with a globally increased follow-up cost    -   the local irritation of the skin created by fixing of the        electrodes in some patients;    -   the position of the electrodes varies from one visit to another,        inducing variations in the reconstructed ECG;    -   the ECG recording is affected by several parameters that are        difficult to control, such as breathing, movements of the        patient, as well as the interferences emitted by various        external electrical sources.

In order to overcome such drawbacks, some algorithms have been developedfor reconstruction of the ECG based upon EGM signals that are directlyprovided by the implanted device. Indeed, reconstruction of the ECGbased upon EGM signals would:

-   -   avoid, during routine visits, having to place surface electrodes        and resort to an ECG recorder;    -   render a patient's visit simpler and quicker, eventually allow        performing a routine visit at the patient's home, and        subsequently shorten the intervals between successive visits,        and improve the patient's follow-up; and    -   allow a remote transmission of the EGM data recorded by the        implanted device, without the intervention of a practitioner or        a medical aid.

Various algorithms for ECG reconstruction based upon EGM signals havebeen previously proposed.

U.S. Pat. No. 5,740,811 (Hedberg, et al.) proposes to synthesize an ECGsignal by combining a plurality of EGM signals by means of a neuralnetwork, fuzzy logic, and/or summer circuit, after a learning process bya “feedforward” type algorithm. This technique does not take intoaccount the propagation time delay between the EGM signals and thesurface ECG signals leading to a precision loss in the reconstructed ECGsignal. Another drawback of such technique is that it does not take intoaccount the varying position of the endocardial leads between the momentof the learning process and that of the use of the device; a change inthe heart electrical axis may bias the synthesized ECG signal,generating a misleading ECG signal. A cardiac disorder that is masked bythe biased synthesis may not be accurately diagnosed.

U.S. Pat. No. 6,980,850 (Kroll et al.) proposes to overcome thisdifficulty, by proposing a method of surface ECG reconstructionimplementing a matrix transform allowing to render each of the ECGderivations individually. Such transform also allows to take intoaccount several parameters, such as patient's respiratory activity orposture that influence tracking the position of the endocardial leadsthrough space. The proposed reconstruction consists of transforming,through a predetermined transfer matrix, an input vector representativeof a plurality of EGM signals into a resulting vector representative ofthe different ECG derivations. The transfer matrix is learned throughaveraging several instantaneous matrices based upon ECG and EGM vectorsrecorded simultaneously over the same period of time.

Although this last technique brings an improvement to that proposed inU.S. Pat. No. 5,740,811, it nevertheless presents certain drawbacks.First, it makes an assumption that there exists a linear relationshipbetween ECG and EGM vectors: such an approximation, though relativelyaccurate with patients presenting a regular rhythm, leads in some casesto large errors of ECG reconstruction in the presence of atypical orirregular signal morphologies—corresponding to potentially pathologiccases. Second, in the presence of noise, it does not provide a uniquesolution for appropriately reconstructing the ECG signals.

The U.S. Pat. No. 7,383,080 and U.S. Patent Publication No. 2008/0065161describes yet another technique for concatenating the ventricular farfield signal (distant signal) observed on the atrium electrode on onehand, with the atrial far field signal (distant signal) observed on theventricular electrode on the other hand to reconstruct an ECG signal. Toconnect the two signals at their concatenation, the process includes astep of subtracting a shift to avoid a mismatch, then multiplying eachsignal by a factor to amplify or attenuate it appropriately.

In the case of a patient with a regular rhythm, this concatenationtechnique is effective because the two far field signals are wellseparated. However, for a patient with an irregular rhythm, thuspotentially pathological, the far field signals are obscured by the Pand R waves and cannot be satisfactorily distinguished from each other.In addition, the proposed processing that simply applies a gain and atime shift reconstructs the ECG signals in a very rough approximationformat, and thus does not reproduce the exact morphology of ECG signals.

EP 1 902 750 A1 and its US counterpart US Patent Publication No. 20080114259(A1) (ELA Medical) describes a technique for reconstruction ofECG using a principal components analysis (PCA) to extract anendocardial vectogram (VGM) from which a surface vectocardiogram isrebuilt (VCG) to obtain, by a reverse transformation, the reconstructedsignals of the different ECG derivations. The reconstruction of the VCGfrom the VGM is made by a learning phase, including use of a neuralnetwork.

These various techniques present certain drawbacks, notably because theEGM and ECG signals, even if they have the same origin, have verydifferent characteristics.

Indeed, electrical activities of a heart reflect the spontaneousstimulations due to the ionic currents in the cardiac cells orartificial stimulations produced by the application of an electricalcurrent to these cells. The EGM (or VGM) signals, directly collected bythe implanted device on one or several derivations, reflect theelectrical potential of the myocardium, whereas the ECG signalscorrespond to the electrical potential recorded on the body surface,over a certain number of derivations, after propagating from themyocardium to this body surface.

A satisfactory reconstruction of ECG signals from EGM signals impliestaking into account the propagation of the electrical phenomena throughthe patient's body, and the dependence of transmembrane potential of theionic currents and of the conductivity of the tissue. These phenomenahave been modeled in various forms, generally known as “bidomainmodels”, that are formulated as nonlinear differential equations of theelectrical potential, containing linear, quadratic and cubic terms.

But the reconstruction techniques described in the documents cited aboverely on a simple linear relationship between EGM and ECG signals,regardless of the physiological knowledge of the bidomain models, withthe exception of techniques using neural networks, which introducenon-linear relationships between the EGM and ECG signals. However, thenon-linearity introduced by the neural network is simply a sigmoidfunction or a limiter, and it is very different from the physiologicalnon-linear bidomain model, reflected by the presence of a quadratic termand a cubic term.

Another drawback, specific to all these techniques is that they can notverify that the reconstruction of ECG signal gives a correct result, andeven less quantify the quality of this reconstruction.

OBJECT AND SUMMARY OF THE INVENTION

It is, therefore, an object of the present invention to reconstruct ECGsignals from the collected EGM signals and to provide a criterion,especially corresponding to an intended use of the reconstructed ECGsignals: for a simple determination of the presence or absence of a peakor a QRS complex the ECG signals are reconstructed with an averagequality, while for an accurate diagnosis based on specific details ofECG or measurements on it, the ECG signals are reconstructed with ahigher quality.

The present invention broadly aims to remedy various drawbacks of priorart techniques by proposing a new technique for reconstruction of ECGsignals from EGM signals with a nonlinear filter that is close tophysiological non-linearity of a bidomain model. A delay representativeof the propagation of electrical signals in body tissues is introduced.

The present invention in a preferred embodiment is based on an approachusing non-linear Volterra filters to represent the relationship betweenEGM signals and ECG signals. The Volterra filters of order 3 introducequadratic and cubic terms and delays, thereby approach in a much morerealistic manner a bidomain model to represent electrical signalpropagation in the patient's body between the myocardium and the bodysurface.

One aspect of the present invention is thus directed to a device forprocessing signals representative of cardiac potential of depolarizationof the myocardium, of the type known according to granted EP 1902750 B1(and its counterpart U.S. Patent Publications 2008/0114257 and2008/0114259) cited above for processing signals representative of acardiac potential of depolarization of the myocardium having means forreconstructing an ECG including: a plurality of inputs, receiving acorresponding plurality of EGM signals from endocardial or epicardialelectrogram, each EGM signal input being acquired on a respective EGMderivation or channel; at least one output, delivering a reconstructedsurface electrocardiogram (ECG) signal related to an ECG derivation; anda digital filter with a non-linear transfer function able to determinesaid ECG signal based on said plurality of EGM signals.

In a manner characteristic of the present invention, the non-lineardigital filter is preferably a Volterra type filter having a transferfunction including a linear term and at least one quadratic and/or cubicterm.

The technique of Volterra filtering in the medical field is alreadyknown, particularly in WO 2008/008692 A2, which describes a Volterrafilter applied to the RR signals representative of the cardiac rhythm.But the heart rate is obtained from the ECG or EGM signals by processesthat are very different from those of the present invention, withoutusing a reconstruction with non-linear filtering. In fact, the prior artis directed to the characterization of a heart rate variability (HRV),which is a specific problem that is unrelated to that of the presentinvention. WO 2008/008692 does not use a Volterra filter for generatinga reconstructed surface electrocardiogram (ECG) signal from EGM signalsdirectly delivered by an implanted prosthesis.

The Volterra filtering is also a very different technology from thatimplemented by the EP 1 902 750 Al cited above because, although thetreatment by a neural network for reconstruction of a VCG from a VGM isof a non-linear type, it resembles in no way a Volterra filtering.Indeed, a neural network applies a nonlinear function only to the valueof the input x[n] at a given time nT (T being the sampling period),while in a Volterra filter, the linear filtering is applied to quadraticor cubic terms using inputs x[n-k] from earlier instants.

Various forms of advantageous present invention include the followings:

The transfer function of the non-linear digital filter preferablycomprises at least a finite time delay (z⁻¹).

In one embodiment, the device includes a plurality of non-linearVolterra filters (12) each receiving as an input an EGM signal(x_(i)[k]) representing the i-th EGM channel or derivation at time k,and delivering as an output a corresponding filtered signal(y_(i,j)[k]), and an adder circuit to combine linearly the filteredsignals output by the plurality of non-linear filters, having as theoutput a reconstructed ECG signal (y_(j)[k]) representing the j-th ECGderivation.

In yet another embodiment, the device includes, for each EGM derivationof a plurality of EGM derivations: a first linear filter receiving as aninput the corresponding EGM signals (x₁[n], x₂[n]), a second linearfilter receiving as an input the same EGM signals squared, and/or athird linear filter receiving as an input the same EGM signals cubed,and means for linearly combining the filtered signals of the first,second and/or third linear filters of each EGM derivation, delivering asan output a reconstructed ECG signal (y[n]). More preferably, the deviceoptionally includes an additional linear filter receiving as an input across product of signals of each EGM derivation; and an adder to combinelinearly, in addition to the filtered signals by the first, and one orboth of the second and third linear filters of each EGM derivation, thesignal delivered by said additional filter.

More preferably, two EGM derivations are used, including an atrial EGMderivation and a ventricular EGM derivation.

In yet another embodiment, the device includes means for concatenatingsequences of samples (x₁[n], x₂[n] . . . x_(Q)[n]) each of them producedat frequency F on each of Q respective EGM derivations, and deliveringas an output a concatenated signal (z[n]) of frequency QF; a nonlinearVolterra filter receiving as an input the concatenated signal (z[n]) anddelivering as an output a corresponding filtered signal (w[n]) offrequency QF, and means for performing a 1/Q down sampling of saidfiltered signal (w[n]), and delivering as an output at a frequency F areconstructed ECG signal (y[n]).

Still another embodiment of the present invention includes means forpredetermining the settings of the digital filter, comprising:

-   -   means for collecting EGM signals and at least one acquired ECG        signal simultaneously, and    -   means for determining parameters of the digital filter, by        minimizing a difference between the acquired ECG signal and a        reconstructed ECG signal from the acquired EGM signals using the        digital filter.

More preferably, the means for determining parameters of the digitalfilter includes means for directly calculating these parameters using analgorithm for computing a matrix solution satisfying a least squaresminimization (LSM) criterion. Alternatively, the means for determiningparameters of the digital filter includes means for implementing analgorithm for computing a matrix solution satisfying a compositecriterion combining the least squares minimization and a Tikhonovregularization.

In another embodiment, the means for determining parameters of thedigital filter include means for iteratively calculating thoseparameters using a recursive least squares (RLS) algorithm with variablestep.

Another aspect of the invention provides the device with means forevaluating the quality of the ECG reconstruction of the non-lineardigital filter, comprising:

-   -   means for simultaneously acquiring EGM signals and at least one        ECG signal;    -   means for determining a reconstructed ECG signal from said        acquired EGM signals, and    -   means for calculating a correlation coefficient between the        acquired ECG signal and the reconstructed ECG signal.

More preferably, the device further includes:

-   -   means for predetermining the settings of the digital filter, and    -   means for validating the determining parameters including means        for comparing to a given threshold the calculated correlation        coefficient and to validate or invalidate those parameters        depending on the outcome of said comparison.

It should be understood that the plurality of inputs may correspond to aplurality of EGM signals acquired from electrodes selected from a groupof: distal and/or proximal right ventricular electrode, distal and/orproximal right atrial electrode, distal and/or proximal left ventricularelectrode, ventricular or atrial defibrillation coil, supra-ventriculardefibrillation coil. Further, the device may be an implantable cardiacprosthesis device selected from a group of stimulation,resynchronization, cardioversion and defibrillation type devices.Alternatively, the device may be an external programmer comprising meansfor downloading and analyzing EGM signals collected by an implanteddevice, or a home monitor, including means for downloading and analyzingEGM signals collected by an implanted device and producing therefromdata, and means for automatic uploading said data to a remote site. Inyet another embodiment, the device may be a data server of a sitereceiving data from a remote monitor for home monitoring including meansfor downloading EGM signals collected by an implanted device, and meansfor automatically transmitting said downloaded EGM signals to saidremote site.

Yet another aspect of the present invention is directed to an apparatusfor reconstructing a surface electrocardiogram (ECG) from a signalrepresentative of a depolarization potential of a myocardium. One suchapparatus includes a plurality of inputs corresponding to a plurality ofelectrogram (EGM) signals from an endocardial or epicardial electrogram(x₁, x₂ . . . x_(Q)), each acquired on one EGM derivation respectively;at least one output corresponding to a reconstructed ECG (y_(j)) for anECG derivation; and a nonlinear digital filter having a transferfunction to determine said reconstructed ECG signal for said given ECGderivation in response to said plurality of inputs, said nonlineardigital filter including a Volterra type filter having a transferfunction including a linear term (h₁) and at least one of a quadraticterm (h₂) and a cubic term (h₃).

The device of the invention thus can be implemented in various formsreferenced above.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features, advantages and characteristics of the presentinvention will become apparent to a person of ordinary skill in the artin view of the following detailed description of preferred embodimentsof the invention, made with reference to the drawings annexed, in whichlike reference characters refer to like elements, and in which:

FIG. 1 is a schematic representation of the technique of reconstructionof an ECG, and of learning of the coefficients of the filters inaccordance with a preferred embodiment of the present invention;

FIG. 2 is a block diagram illustrating an implementation of a Volterrafilter of order 2 for a system with one input and one output;

FIG. 3 is a block diagram of a first embodiment of the presentinvention, allowing the reconstruction of an ECG derivation from threeEGM channels;

FIG. 4 is a block diagram of a second embodiment of the presentinvention, allowing the reconstruction of an ECG derivation from anatrial and a ventricular EGM channel; and

FIG. 5 is a block diagram of a third embodiment of the presentinvention, allowing the reconstruction of an ECG derivation using asingle Volterra filter.

DETAILED DESCRIPTION OF THE INVENTION

With reference to the drawings FIGS. 1-5, several examples ofimplementations of preferred embodiments of the present invention willnow be described. Preferably, the functionality and processes of thepresent invention as described herein can be implemented by anappropriate programming of software of a known implantable pulsegenerator, for example, a pacemaker or defibrillator/cardioverter,comprising known and conventional circuits and signal acquisition andprocessing algorithms for acquiring a signal provided throughendocardial leads and/or several implanted sensors.

The invention can advantageously be applied to and implemented in thecommercial implantable devices marketed by Sorin CRM, Montrouge France,such as the Reply™ and Paradym™ brand pacemakers and comparablecommercial and/or proprietary devices of other manufacturers. Thesedevices are equipped with programmable microprocessors, includingcircuits intended to acquire, condition and process electrical signalscollected by implanted electrodes and various sensors, and deliverpacing pulses to implanted electrodes. It is also possible to uploadtowards these devices, by telemetry, pieces of software (i.e., asoftware control module) that will be stored in internal memory and runso as to implement the features and functionality of the presentinvention, as described herein. Implementing the features of theinvention into these devices is believed to be easily within theabilities of a person of ordinary skill in the art, and will thereforenot be described in detail.

The invention may be implemented within an implant (i.e., direct dataprocessing of the EGM signals by the implanted device), but it may alsobe implemented in an external programmer used by a practitioner bydownloading and analyzing the cardiac signals collected and memorized byan implant.

In yet another advantageous preferred embodiment, the invention isimplemented in a home monitor. The home monitor is a special type ofprogrammer whose operation is essentially fully automated withoutrequiring a practitioner. It is particularly intended to allowtransmission at regular intervals to a remote site of the collected andanalyzed data, e.g. daily, in order to monitor the cardiac condition ofthe patient remotely.

The invention may also be implemented at a server located at a remotesite. For example, the raw EGM data from the implanted device isuploaded to the remote site server directly, without prior processing.The processing is performed by the remote server or a terminal (e.g., aPC computer or programmer) that implements the present invention.

A. Collection of the EGM Signals

The EGM signals are acquired on a plurality of “channels”, each channelcorresponding to a pair of endocardial or epicardial electrodesconnected to the housing of the implanted cardiac device. These channelsalso are known as “derivations”.

The choice of electrodes defining these channels depends on theconsidered implanted cardiac prosthesis, for example, pacemaker (fortreatment of bradycardia), defibrillator (for treatment of tachycardiaand fibrillation) or resynchronizer (for treatment of heart failure).Three modes of cardiac stimulation are distinguished: single, dual ortriple chamber. These different functions correspond to different choiceof electrodes, and to a number of EGM signals different in eachsituation.

As used herein “RV”, “RA” and “LV”, respectively, designate the rightventricular, right atrial and left ventricular electrodes of theintracardiac leads with a “+” or “−” sign indicating the distal orproximal position of the electrode, and “CoilV” and “SVC” respectivelydesignate the ventricular and supraventricular defibrillation coils.Thus, the possible combinations of electrodes are (with each time, thepossibility to select a bipolar configuration by considering thedifference between two electrodes or to select an unipolar configurationby considering the difference between one electrode and the generatorhousing or CAN):

-   -   single chamber: RV+, RV− (and CoilV and in the case of a        defibrillator), a single chamber pacemaker provides two EGM        signals through the distal and proximal electrodes, the ground        being taken on the CAN. The version in a defibrillator delivers        three EGM signals through the added CoilV electrode.    -   dual chamber: RV+, RV−, RA+, RA− (and CoilV and SVC in the case        of a defibrillator), a dual-chamber pacemaker provides four EGM        signals, and six in a defibrillator version.    -   triple chamber: RV+, RV−, RA+, RA−, LV+, LV− (and CoilV and SVC        in the case of a defibrillator), a triple chamber pacemaker        provides six EGM signals, and eight in a defibrillator version.

B. Principle of Reconstruction of the ECG

The ECG signals, which are the manifestation of the cardiac electricalactivities on the surface of the patient's body, are well known andnormally collected between pairs of electrodes applied in predeterminedlocations of the patient's chest. Each pair of electrodes determines a“derivation”. The whole forms a set of twelve derivations, includingbipolar derivations (I, II, III), unipolar derivations (aVF, aVR, aVL)and precordial derivations (V1 to V6).

According to one embodiment, the present invention reconstructs one ormore of these ECG signals from the signals collected in the form of aplurality of EGM derivations. The basic principle of this reconstructionis schematically shown in FIG. 1. A plurality of EGM signals x₁, x₂ . .. x_(Q), are collected and sampled on Q EGM channels (10). Each of thesesignals is applied to a respective filter F₁, F₂ . . . F_(Q), (reference12). The output signals of each of these filters 12 are linearlycombined in adder 14 to produce a reconstructed ECG signal 16,corresponding to one of the twelve derivations to be reconstructed. Thereconstructed signal 16 on the derivation No. j will be designatedy_(j). Other ECG derivations are reconstructed by the same technique buttypically with different filter settings.

The setting of the filters corresponding to an ECG derivation isachieved by a learning process that includes comparing the reconstructedECG signal 16 to an ECG signal 18 actually measured on the consideredderivation. These two signals are applied to a linear differentiator 20delivering an error signal 22 to ensure, through learning, an adaptationand setting of filters 12. This stage of learning, which will beexplained in more detail in the following description, is essentially tocalculate, for each of the filters F₁, F₂ . . . F_(Q), the parameters(i.e., coefficients) of these filters that minimize the differencebetween the reconstructed ECG and the ECG actually measured.

C. Principle of Volterra Filtering

In a preferred embodiment of the invention, filters F₁, F₂ . . . F_(Q)are Volterra type non-linear filters. The Volterra filter is described,for example by Schetzen M, “The Volterra and Wiener Theories ofNonlinear Systems,” Wiley and Sons, New York, 1980, or by V J Mathews,“Adaptive Polynomial Filters”, IEEE Signal Processing Magazine, 8 (3)pp. 10-26, July 1991. Volterra filters allow in particular establishinga non-linear relationship between the EGM signals and the ECG signalssimilar to the one of a bidomain model that includes linear, quadraticand cubic terms. They also introduce in this relationship a finite delayreflecting the propagation of the electrical signals through bodytissues from the myocardium to the surface of the patient's skin.

Specifically, a Volterra filter receives as input discrete real timesignal x[n], with n being an integer (n being the rank of the samplesignal), and generates an output y[n] defined by:

${y\lbrack n\rbrack} = {h_{0} + {\sum\limits_{m = 1}^{p}{\sum\limits_{k_{1} = 0}^{N_{1} - 1}\mspace{14mu} {\ldots \mspace{14mu} {\sum\limits_{k_{p} = 0}^{N_{m} - 1}{{h_{m}\left\lbrack {k_{1},\ldots \mspace{14mu},k_{m}} \right\rbrack}{x\left\lbrack {n - k_{1}} \right\rbrack}\mspace{14mu} \ldots \mspace{14mu} {x\left\lbrack {n - k_{m}} \right\rbrack}}}}}}}$

This equation defines an input-output relationship of a Volterra filterof the p-th order.

In the following description, the order of the Volterra filter islimited to p=3, but it should be understood that this simplification isin no manner a limitation and the invention also contemplates the use ofhigher order filters. In the embodiment of order p=3, the above equationbecomes:

${y\lbrack n\rbrack} = {h_{0} + {\sum\limits_{k = 0}^{N_{- 1}}{{h_{1}\lbrack k\rbrack}{x\left\lbrack {n - k} \right\rbrack}}} + {\sum\limits_{K = 0}^{P - 1}{\sum\limits_{l = 0}^{P - 1}{{h_{2}\left\lbrack {k,l} \right\rbrack}{x\left\lbrack {n - k} \right\rbrack}{x\left\lbrack {n - 1} \right\rbrack}}}} + {\sum\limits_{k = 0}^{M - 1}{\sum\limits_{l = 0}^{M - 1}{\sum\limits_{r = 0}^{M - 1}{{h_{3}\left\lbrack {k,l,r} \right\rbrack}{x\left\lbrack {n - k} \right\rbrack}{x\left\lbrack {n - 1} \right\rbrack}{x\left\lbrack {n - r} \right\rbrack}}}}}}$

This equation can be simplified as:

y[n]=h ₀ +h ₁(N)+h ₂(P)+h ₃(M)

where h_(o) is a constant term, independent of the input, h₁ is a linearfilter, h₂ a quadratic filter and h₃ a cubic filter (the term h_(m) iscalled “kernel of order m” filter). It should be understood that such afilter is causal, since it only involves the previous values at time n.Here, N represents the “memory” of the linear filter h₁, correspondingto more or less the important part of the past of the inputs involved inthe construction of the present output, P and M representing, in thesame way, the memory of quadratic h₂ and cubic h₃ filters. In thepublished literature, Volterra filters generally have identical memoriesN, M and P, but in the case of the present invention, it is preferableto use different memory for each kernel h_(m) in order to reduce certainkernels memory and hence reducing the overall complexity of computing.

With reference to FIG. 2, details are illustrated of an embodimentimplementing a Volterra filter of second order. For simplicity, thepresent example does not have a constant term. This filter 12 comprisesan input x[n] and an output y[n].

The linear kernel 24 (term h₁) acts directly on the input signal Thequadratic kernel 26 (term h₂) has P linear filters 28, 30, 32, and soon. The first linear filter 28, h_(2,0) of the quadratic kernel 26 actson the signal x[n] multiplied by itself, that is x[n]x[n]=x²[n] Thesecond linear filter 30, h_(2,1) of the quadratic kernel 26 acts on thesignal x[n] multiplied by that same signal delayed by one sample. Theoperator z⁻¹ of the block 34 represents a delay of one sample. The inputof the second linear filter 30 is the signal x[n] . . . x[n-1]. Thisprocess repeats and the last linear filter h_(2,p-1) of the quadratickernel 26 acts on the signal x[n] . . . x[n-P-1].

In its general form, the quadratic filter h₂ is a PxP matrix oftwo-dimensional elements, and the filter cube h₃ is a three-dimensionalmatrix of MxMxM elements. If one eliminates from these matrices theredundant terms, the number of coefficients is reduced, and the generalequation of a Volterra filter of third order becomes:

${y\lbrack n\rbrack} = {h_{0} + {\sum\limits_{k = 0}^{N - 1}{{h_{1}\lbrack k\rbrack}{x\left\lbrack {n - k} \right\rbrack}}} + {\sum\limits_{k \geq 1}^{P - 1}{\sum\limits_{l = 0}^{P - 1}{{h_{2}\left\lbrack {k,l} \right\rbrack}{x\left\lbrack {n - k} \right\rbrack}{x\left\lbrack {n - 1} \right\rbrack}}}} + {\sum\limits_{k \geq 1}^{M - 1}{\sum\limits_{l \geq r}^{M - 1}{\sum\limits_{r = 0}^{M - 1}{{h_{3}\left\lbrack {k,l,r} \right\rbrack}{x\left\lbrack {n - k} \right\rbrack}{x\left\lbrack {n - 1} \right\rbrack}{x\left\lbrack {n - r} \right\rbrack}}}}}}$

Note that if h₀=0 and if P=0 and M=0 (i.e., no memory of the past forquadratic and cubic kernels), this equation is reduced to a conventionalconvolution of a transverse linear filter, also known as a finiteimpulse response (FIR) filter.

D. First Mode of Implementation of the Invention

In the case of a reconstruction of ECG signals from EGM, the systemreceives multiple inputs depending on the number measurable by theimplant EGM channels and outputs one or more ECG derivations (e.g., fromone to twelve depending on the number of desired). Such a system is ofmulti-input/multi-output (MIMO) type.

To simplify the discussion below, each ECG derivation will be consideredseparately, and the reconstruction of one ECG derivation from aplurality of input EGM channels (a multi-input/single output (MISO)system) is described below. The reconstruction method can obviously begeneralized to a plurality of ECG derivations, each with its own filtercoefficients.

This first implementation is made with reference to FIG. 3. A Volterrafilter (filter 12) is applied to each EGM derivation 10. The outputs offilters 12 are subjected to a linear combination using adder 14 toreconstruct the ECG derivation from all the filtered channels.

If we designate x_(i)[k] the discrete signal of the EGM channel No. i,and h_(m) ^(i,j) the Volterra filter kernel of order m driven by thissignal x_(i)[k] to reconstruct the signal y_(j)[k] representing the ECGderivation (reconstructed) n^(o)j, the output y_(i,j)[k] of the Volterrafilter 12 is given by:

${y_{i,j}\lbrack n\rbrack} = {h_{0}^{i,j} + {\sum\limits_{k = 0}^{N - 1}{{h_{1}^{i,j}\lbrack k\rbrack}{x_{i}\left\lbrack {n - k} \right\rbrack}}} + {\sum\limits_{k \geq 1}^{P - 1}{\sum\limits_{l = 0}^{P - 1}{{h_{2}^{i,j}\left\lbrack {k,l} \right\rbrack}{x_{i}\left\lbrack {n - k} \right\rbrack}{x_{i}\left\lbrack {n - 1} \right\rbrack}}}} + {\sum\limits_{k \geq 1}^{M - 1}{\sum\limits_{l \geq r}^{M - 1}{\sum\limits_{r = 0}^{M - 1}{{h_{3}^{i,j}\left\lbrack {k,l,r} \right\rbrack}{x_{i}\left\lbrack {n - k} \right\rbrack}{x_{i}\left\lbrack {n - 1} \right\rbrack}{x_{i}\left\lbrack {n - r} \right\rbrack}}}}}}$

The signal y_(j)[k] of the ECG derivation n^(o)j reconstructed from theQ signals y_(i,j)[k] is given by:

${y_{j}\lbrack n\rbrack} = {\sum\limits_{i = 1}^{Q}{y_{i,j}\lbrack n\rbrack}}$

It is demonstrated that the number of unknowns to be determined toreconstruct a (unique) ECG derivation from Q EGM channels is equal to:

K ₁=1+Q[N+P(P+1)/2+M(M+1)(M+2)/6]

It is possible to cancel some kernels h_(m) to reduce the number ofunknowns in the system to solve, for example, by using only quadraticVolterra filters of order 2, with M=0. Alternately, one may choose tocancel the quadratic term (P=0) and keep the cubic term.

E. Second Mode of Implementation of the Invention

The second embodiment of the present invention uses a simplified versionof the Volterra filter to take into account the productsx_(i)[n-k]x_(i)[n-1] between the temporal samples of the same inputsignal x_(i)[k] taken at the same sampling moments. This is equivalentto apply linear filters to their squares x_(i)[k]x_(i)[k]=x_(i) ²[k] . .. (diagonal terms of the kernels h_(m)).

The contribution of the signal x_(i)[k] of the EGM derivation n^(o) i inthe construction of the ECG derivation y[k] is then:

${y_{i}^{\prime}\lbrack n\rbrack} = {h_{0}^{i} + {\sum\limits_{k = 0}^{N - 1}{{h_{1}^{i}\lbrack k\rbrack}{x_{i}\left\lbrack {n - k} \right\rbrack}}} + {\sum\limits_{k = 0}^{P - 1}{{h_{2}^{i}\lbrack k\rbrack}{x_{i}^{2}\left\lbrack {n - k} \right\rbrack}}} + {\sum\limits_{k = 0}^{M - 1}{{h_{3}^{i}\lbrack k\rbrack}{x_{i}^{3}\left\lbrack {n - k} \right\rbrack}}}}$

With this simplified version, it may be advantageous to also take intoaccount the cross-products x_(c)[k] between several EGM inputs on thesame sampling moments. In this case, the equation of the reconstructedECG signal is:

x_(c)[k] = x₁[k]x₂[k]  …  x_(Q)[k]${y\lbrack k\rbrack} = {{\sum\limits_{i = 1}^{Q}{y_{i}^{\prime}\lbrack n\rbrack}} + {\sum\limits_{s = 0}^{N - 1}{{h_{c}\lbrack s\rbrack}{x_{c}\left\lbrack {n - k} \right\rbrack}}}}$

The number of unknown variables is: 1 for the constant term, QN for thelinear term, QP for the quadratic term, QM for the cubic term and N forthe cross product term, or K₂=1+N+Q(N+P+M) unknowns to be determined.

With reference to FIG. 4, the block diagram illustrates the secondimplementation with two input EGM channels, namely:

-   -   the signal x₁[n] representing the EGM collected by a lead        located in an atrium, and    -   the signal x₂[n] representing the EGM collected by a lead        located in a ventricle.

The block 12′ represents a first simplified Volterra filter, acting onthe diagonal terms only. It contains three linear filters 24, 26, 40representing the three kernels of that filter, which respectivelyreceive the signal x₁[n], its square 42, and its cube 44. Block 12″performs the same operations respectively on the signal x₂[n].

The filter 46 is a linear filter that receives as an input the crossproduct 48 of x₁[n] and x₂[n] signals; x₁[n] is the signal collected inthe atrium and x₂[n] is the signal collected in the ventricle; the crossproduct x_(c)[k]=x₁[k]x₂[k] is a signal close to the far-field signalbecause the signal x₂[n]is attenuated everywhere except at the momentswhen the P wave occurs; and the signal x₁[n] is reduced everywhereexcept at the moments when the R wave occurs. In other words, the signalx_(c)[k] represents the signal acquired by the atrial lead, amplified atthe moments when the R wave occurs.

The ECG signal is calculated by an adder 14 making a linear combinationof outputs of Volterra filter 12′ and 12″ and of the output h_(c), offilter 46 (the constant term h₀ is omitted in this figure). Thissimplified version has the advantage of a reduced complexity as comparedto the full version of the first implementation, taking into accountnon-linearity of a bidomain model.

As in the case of the first implementation, it is possible to furtherreduce the complexity of the Volterra filter of the secondimplementation by cancelling some kernels of order 2 or 3 in particular.

F. Third Mode of Implementation of the Invention

The third embodiment implementing the present invention uses only oneVolterra filter for the reconstruction of an ECG derivation,irrespective of the number Q of EGM channels. The technique, illustratedwith reference to FIG. 5, is to produce a signal z[n] consisting of aconcatenation of successive EGM signals x_(i)[n]=x₁[n], x₂[n] . . .x_(Q)[n]. For each sampling instant nT, the signal z is built using allthe Q values of signals x_(i)[n]. Thus, if the sampling frequency of theEGM signals is F, the frequency of the signal z[n] is equal to QF.

According to one embodiment, the function 50 is implemented by aparallel to series converter, or by a circular switch 50 switchingbetween the Q input signals at a frequency QF.

Volterra filter 12 is applied to the signal z[n] thus formed, andproduces an output signal w[n], also at the frequency QF.

The signal y[n] at frequency F, is extracted from the signal w[n] bydown-sampling of order Q by keeping a value every Q values (block 52).

This implementation involves cross products between the values ofvarious input signals, taken at different sampling instants. SinceVolterra filter 12 works at frequency QF it requires Q times morememory, to cover the same past of the signal, than the same filteroperating at frequency F.

The number of unknowns to be determined to reconstruct an ECG derivationfrom Q EGM channels is:

K ₃=1[QN+QP(QP+1)/2+QM(QM+1)(QM+2)/6]

The complexity of Volterra filter 12 is mainly based on the number ofchannels Q of EGM derivations in input.

G. Determination of Coefficients of Volterra Filters

As stated above, the determination of the coefficients of the Volterrafilters used to reconstruct the ECG is based on a learning processoperated in a first step by collecting simultaneously a set of referencedata consisting of EGM signals x_(j) ^(R)[k] and of ECG signals y^(R)[k]synchronized with the EGM signals.

The number of unknowns to be determined in the system depends on thesize of N, P and M memories of the filters, and the length of thetraining sequence should be sufficient for an unambiguous determinationof the filter coefficients (greater than the number of unknowns in theVolterra system).

The filtering equations developed above are expressed in a simpler form.The basic idea is that the output is generally linear in terms of theparameters h, although it is not linear in input x. This allows to writethe input-output relationship as a scalar product of properly definedvectors.

In the case of the first embodiment of implementation of the invention,a vector of unknowns H, of size K, defined above, is formed by theconcatenation of several sub-vectors hint, each representing thecoefficients of the kernel of order m driven by the EGM derivationsignal No. i:

H=[h ₀ , h ₁ ¹ , h ₂ ¹ , h ₃ ¹ , . . . , h ₁ ^(Q) , h ₂ ^(Q) , h ₃^(Q)]^(T)

This simplification of the kernels is reused for the input signal. Inparticular, the vector x_(i)[n]={x_(i)[n], . . . , x_(i)[n-N-1]} of theEGM input No. i is associated to the vector x_(m) ^(i) representing thenon-redundant terms implied in the kernel of order m:

x ₁ ^(i) [n]=x _(i) [n]

x ₂ ^(i) [n]={x _(i) [n-k]x _(i) [n-1]}_(P>k≧1≧0)

x ₃ ^(i) [n]={x _(i) [n-k]x _(i) [n-1]x _(i) [n-r]} _(M>r≧k≧1≧0)

A global vector X representing the total contribution of all Q EGMinputs:

X[n]=[1, x ₁ ¹ [n], x ₂ ¹ [n], x ₃ ¹ [n], . . . , x ₁ ^(Q) [n], x ₂ ^(Q)[n], x ₃ ^(Q) [n]] ^(T)

The constant 1 represents the input signal to the constant term h₀ ofthe filter.

The input-output relationship described above for the first embodimentof implementation takes a simplified form:

y[n]=X[n]^(T)H

In the case of second and third modes of implementation, the equationsare transformed into a scalar product of two vectors, namely a vector Hcontaining the filter coefficients and a vector X containing quantitiescalculated from products formed between the input values for differentsampling instants.

H. Determination of Filter Coefficients (First Technique—RegularizationTikhonov)

With a reference set containing EGM signals and ECG signals acquiredsimultaneously, the above equation allows to deduce the filter H thatbest fits this equation. Several techniques may be implemented toachieve this result.

A first matrix technique is to transform the previous vector equation toa matrix equation, using all data. Assuming that the dataset has alreadybeen acquired before, the conversion can be done offline (batch mode).Let L be the size of data set reference, and n₀=max(N,P,M) the maximummemory of the kernels of the Volterra filter. We now have L-n₀ vectorequations that are grouped as:

$\begin{bmatrix}{y^{R}\left\lbrack n_{0} \right\rbrack} \\\vdots \\{y^{R}\lbrack n\rbrack} \\\; \\{y^{R}\left\lbrack {L - n_{0}} \right\rbrack}\end{bmatrix} = {\begin{bmatrix}{X_{R}\left\lbrack n_{0} \right\rbrack}^{T} \\\vdots \\{X_{R}\lbrack n\rbrack}^{T} \\\vdots \\{X_{R}\left\lbrack {L - n_{0}} \right\rbrack}^{T}\end{bmatrix}H}$ Or $Y = {\overset{\_}{A}H}$

-   Y being a vector of L-n₀ values of a given ECG derivation,-   Ā being a matrix of (L-n₀) x K₁ non-redundant elements formed from    the EGM inputs, and H being a vector of K₁ unknowns representing the    Volterra filter coefficients.

The fact that the matrix Ā is composed of elements that are not formallyredundant does not guarantee that it is numerically well conditioned toensure a unique and stable solution H obtained in solving the linear (inH) system above. Note also that the values of ECG in Y and the EGMvalues used in Ā are affected by various types of noise. This makes thelinear system an “ill-posed inverse problem” in the sense that thematrix Ā is a “ill-conditioned matrix”.

The least squares solution of the linear system that minimizes the normof the difference between the values Y of the acquired ECG and the ECGvalues calculated by the solution H_(LS) is given by:

H _(LS)=(Ā ^(T) Ā)⁻¹ Ā ^(T) Y

This solution H_(LS) minimizes the least squares criteria ∥Y-ĀH∥².

To ensure a numerically stable solution, the present invention proposesto use a regularization that finds a solution satisfying a compositecriterion, by adding a constraint to the constraint of the leastsquares. This regularization, known as a “Tikhonov regularization”, isdescribed as a general principle, especially by A N Tikhonov and V AArsenin, “Solution of Ill-Posed Problems,” Winston & Sons, Washington,1977 (ISBN 0-470-99124-0). The composite criterion used is written:

∥Y−ĀH∥²+λ∥ ΓH∥²

Where Γ is the Tikhonov matrix. Often this matrix is chosen as theidentity matrix Γ=1, to favour solutions with a low norm and hence toensure numerical stability. In other cases, the matrix Γ may present anoperator of first order difference

to obtain smooth solutions. The parameter λ is called the regularizationparameter and represents a tradeoff between the least squares criterionand the additional Tihkonov criterion. The regularized solution is givenby:

H _(Tikh)=(Ā ^(T) Ā+λ Γ ^(T) Γ)⁻¹ Ā ^(T) Y

Several techniques for choosing the regularization parameter λ can befound in the literature, the method of “cross validation” being the mostcommon.

This first technique for determining the coefficients of the Volterrafilter provides a high quality of reconstruction. However, it may not bepractical in a real time application because it requires the combinationof the reference EGM data in a matrix. It also requires a relativelylarge memory because the size of the formed matrix depends on the sizeof the reference data. It is therefore preferably implemented in aprogrammer communicating with the implant and having a fast processorand large memory size.

I. Determination Of Filter Coefficients (Second Technique—RecursiveLeast Squares)

Another technique that is used to determine the coefficients of thefilter is the Recursive Least Squares (RLS). An example of this methodis described by Hayes, M H (1996), “Recursive Least Squares, StatisticalDigital Signal Processing and Modeling,” Wiley, p. 541 (ISBN0-471-59431-8), or by S Haykin, Adaptive Filter Theory, Prentice Hall,2002 (ISBN 0-13-048434-2).

This approach solves linear system y[n]=X[n]^(T)H in real-time(on-line), and requires less computational resources for calculating thecoefficients. It is therefore implemented in an implanted device withoutthe need for an external programmer. This iterative method uses avariable step to control the convergence speed during iterations, whichrepresents an advantage in multi-input systems compared to iterativemethods with fixed step like LMS. The RLS forgetting factor plays therole of the regularization of the matrix method of Tikhonov.

J. Assessing the Quality of the Reconstruction of the ECG

Another aspect of the present invention concerns assessing the qualityof the reconstruction of the ECG. The quality of the reconstruction isestimated, for example, to choose a particular reconstruction techniquebased on an acceptable tradeoff between hardware limitations(computation time, hardware and software resources available) and theactual needs according to the intended use of the reconstructed ECG(e.g., detecting the mere presence of certain characteristics, orfurther examination of waveforms).

To assess the quality of the reconstruction, the EGM and ECG signals(ECG signals that are actually collected) are acquired simultaneouslyduring a measurement period T_(m). This period T_(m) must be at leasttwo cardiac cycles long (approximately 2 s) and may be extended up to100 or 1000 seconds. The sequences chosen as a set of reference data forthe learning process has duration T_(r) of at least one second and canbe extended up to 99 or 999 seconds. The EGM and ECG signals areacquired simultaneously during a period T_(m) for example, with asampling rate of 128 Hz.

If the sampling frequency of the ECG and EGM (usually located in therange 100 Hz to 1 kHz) are different, it is necessary to synchronize thedata by a suitable technique, such as interpolation (linear, polynomialor splines) or com-pression (e.g., turning point Mueller algorithm).

The quality of the reconstruction of the ECG signals is evaluated by anumerical criterion that involves determining, for a sequence that hasnot been used for the learning process, the correlation coefficient pbetween the real ECG signals y[k] and the reconstructed ECG signalsy_(rec)[k].

Specifically, a shift or a time delay in the order of 40 ms (i.e., ashift of d=5 samples for a sampling frequency of 128 Hz) in thereconstructed signal does not alter the capacity to diagnose the ECGsignals.

The correlation coefficient is evaluated for each shift k:

$\rho_{k} = \frac{\sum\limits_{i = 0}^{J}{\left( {{y\lbrack i\rbrack} - \overset{\_}{y}} \right)\left( {{y_{rec}\left\lbrack {i + k} \right\rbrack} - {\overset{\_}{y}}_{rec}} \right)}}{\sqrt{\sum\limits_{i = 0}^{J}\left( {{y\lbrack i\rbrack} - \overset{\_}{y}} \right)^{2}}\sqrt{\sum\limits_{i = 0}^{J}\left( {{y_{rec}\left\lbrack {i + k} \right\rbrack} - {\overset{\_}{y}}_{rec}} \right)^{2}}}$

The quality of reconstruction (between −1 and +1) is estimated by:

$\rho = {\max\limits_{{- d} \leq k \leq d}\left( \rho_{k} \right)}$

For ECG sequences that have a regular rhythm, the present inventionprovides a quality reconstruction superior to 97% from bipolar signalsfrom the atrium and from the ventricle (the proximal signal beingconsidered by reference to the distal signal). The reconstructed ECGsignals faithfully reproduce the polarity, width and position of the QRScomplex in the ECG.

The quality of reconstruction obtained by the present invention is veryhigh in comparison to that obtained with methods based on known neuralnetworks, which is only about 85% when using two bipolar, atrial andventricular, signal for a patient having a regular cardiac rhythm.Specifically, the quality of reconstruction should be of the order of atleast 60 to 65% in order to find in the reconstructed ECG certainpeculiarities that we look to determine its presence or absencelike(peaks, polarity, etc . . . ). These peculiarities may be sufficientfor a quick patient follow-up visit for ECG monitoring. However, inorder to establish a more accurate diagnosis from a detailed examinationof waveforms, the quality of reconstruction should be at least about80%.

The quantified quality of reconstruction is especially used to validatethe calculation of the filter coefficients in the learning process.Thus, after calculating the filter parameters, the quality ofreconstruction is compared to a threshold value. This threshold isprogrammable and is adjusted if necessary by the practitioner, or ispreset to an acceptable value, e.g. 65%.

If the quality criterion is verified (threshold is exceeded), theestimated coefficients are stored, and the calculated filter is used forlater reconstruction of the considered ECG derivation. The process isoptionally repeated for each ECG derivation to be used. However, if thecriterion is not verified, it is necessary to restart the determinationof the filter parameters, either by selecting a different referenceperiod T_(r) in the measurement window T_(m) (in the window T_(r), therewere perhaps arrhythmias that might interfere with the learningprocess), or by repeating the acquisition of another data set overanother length T_(m).

One skilled in the art will appreciate that the present invention can beprotected by embodiments other than those described herein, which areprovided for purposes of illustration and not of limitation.

1. A device for reconstructing a surface electrocardiogram (ECG), thedevice comprising: a first linear filter receiving an inputcorresponding to endocardial or epicardial electrogram (EGM) signals; asecond linear filter receiving the EGM signals squared, and/or a thirdlinear filter receiving the same EGM signals cubed; and a linearcombination of the filtered signals from the first, second and/or thirdlinear filters of each EGM derivation, delivering as an output areconstructed ECG signal.
 2. The device of claim 1, comprising:receiving an additional linear filter optionally as an inputcorresponding to the EGM signals in each derivation.
 3. The device ofclaim 2, comprising: linearly combining the filtered input signals by anadditional linear filter with the filtered signals by the first, and oneor both of the second and third linear filters in each EGM derivation.4. The device of claim 1, comprising: using two EGM derivations as theinputs to reconstruct the ECG, including an atrial EGM derivation and aventricular EGM derivation.
 5. The device of claim 4, comprising:acquiring EGM signals through different electrode combinations of thebipolar configurations and three heart chambers, including the rightventricular, right atrial and left ventricular.
 6. The device of claim1, comprising: applying all the linear filters with predeterminedcoefficients.
 7. The device of claim 1, comprising: directing to anapparatus for reconstructing a surface ECG from a signal representativeof a depolarization potential of a myocardium.
 8. The device of claim 7,wherein the apparatus includes a plurality of inputs corresponding to aplurality of EGM signals from endocardial or epicardial electrogram,each acquired on one EGM derivation respectively.
 9. The device of claim8, further comprising: delivering an output with at least one outputcorresponding to a reconstructed ECG for an ECG derivation.
 10. Thedevice of claim 9, comprising: determining the output by a nonlineardigital filter including a Volterra type filter having a transferfunction including a linear term and at least one of a quadratic termand a cubic term.
 11. A method predetermining the settings of a digitalfilter, comprising: collecting epicardial electrogram (EGM) signals andat least one acquired electrocardiogram (ECG) signal simultaneously, anddetermining parameters of the digital filter, by minimizing a differencebetween the acquired ECG signal and a reconstructed ECG signal from theacquired EGM signals using the digital filter.
 12. The method of claim11, comprising: determining parameters of the digital filter by using analgorithm to compute a matrix solution to minimize the differencebetween the acquired ECG and the ECG values calculated by theapproximated solution criterion.
 13. The method of claim 12, comprising:using a least squares minimization method or a combination of the leastsquares minimization method and a Tilhonov regularization method todetermine the matrix solution as the predetermined parameters of thedigital filter.
 14. The method of claim 13, comprising: using a crossvalidation approach to choose the regularization parameter in theTilhonov regularization criterion.
 15. The method of claim 13, furthercomprising: determining parameters of the digital filter using a leastsquares minimization method including a iterative calculation using arecursive least squares (RLS) algorithm with variable steps.
 16. Amethod for evaluating the quality of an electrocardiogram (ECG)reconstruction of a non-linear digital filter, comprising: acquiringepicardial electrogram (EGM) signals and at least one ECG signal;determining a reconstructed ECG signal from said acquired EGM signals,and calculating a correlation coefficient between the acquired ECGsignal and the reconstructed ECG signal.
 17. The method of claim 16,comprising: simultaneously acquiring the ECG and EGM signals during aperiod T_(m) by synchronizing the ECG and EGM signals with same samplingfrequency though interpolation or compression.
 18. The method of claim16, comprising: predetermining the settings of the digital filter basedon the calculated correlation coefficient.
 19. The method of claim 16,further comprising: validating the determined parameters includingcomparing to a given threshold the calculated correlation coefficientand validating or invalidating those parameters depending on the outcomeof said comparison.
 20. The method of claim 19, comprising: storing thevalid estimated coefficients and the calculated filter to use for futurereconstruction of the considered ECG derivation.